Function `g(x)=int_- 3^xsint(1/2-cost)dt` where `0 < x < 2pi,` has

For the function f(x)=int_(0)^(x)(sin t)/(t)dt where x>0

Find the range of the function f (x) = int _(0) ^(x) |t-1| dt, where 0 le x le 2

The difference between the greatest and the least values of the function f(x) = int_0^x (at^2 + 1 + cost)dt, a > 0 for x in [2, 3] is

The difference between the greatest and the least values of the function f(x)=int_(0)^(x)(at^(2)+1+cos t)dt,a>0 for x in[2,3] is

Which of the following is/are true for the function f(x)= int _(0) ^(x) ("cost")/(t ) dt (x gt 0) ?

Which of the following is/are true for the function f(x)= int _(0) ^(x) ("cost")/(t ) dt (x gt 0) ?

Statement I The function f(x) = int_(0)^(x) sqrt(1+t^(2) dt ) is an odd function and STATEMENT 2 : g(x)=f'(x) is an even function , then f(x) is an odd function.

Statement I The function f(x) = int_(0)^(x) sqrt(1+t^(2) dt ) is an odd function and STATEMENT 2 : g(x)=f'(x) is an even function , then f(x) is an odd function.

Statement I The function f(x) = int_(0)^(x) sqrt(1+t^(2) dt ) is an odd function and g(x)=f'(x) is an even function , then f(x) is an odd function.

Let f be continuous and the function g is defined as g(x)=int_0^x(t^2int_1^t f(u)du)dt where f(1) = 3 . then the value of g' (1) +g''(1) is